%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% File:               Paramsls.m
%
% Authors:            Sergio Ascencio and Miguel Rueda
%
% Language:           MATLAB R2013b (8.2.0.701) 64 Bit
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


function beta=Paramsls(Y,X,phats,beta_p)

%Extended
% varsx={'l_d_RC_others' 'l_margin' 'lcasillas' 'school_ic' 'l_diff_PRI_PAN' 'lpop' 'l_turnout' 'local' 'ldist_city' ...
% 'l_d_RC_others_sq' 'l_margin_sq' 'lcasillas_sq' 'school_ic_sq' 'l_diff_PRI_PAN_sq' 'lpop_sq' 'l_turnout_sq' 'ldist_city_sq' ...
% 'l_d_RC_others_l_margin' 'l_d_RC_others_lcasillas' 'l_d_RC_others_school_ic' 'l_d_RC_others_l_diff_PRI_PAN' 'l_d_RC_others_lpop' 'l_d_RC_others_l_turnout' 'l_d_RC_others_local' 'l_d_RC_others_ldist_city' ...
% 'l_margin_lcasillas' 'l_margin_school_ic' 'l_margin_l_diff_PRI_PAN' 'l_margin_lpop' 'l_margin_l_turnout' 'l_margin_local' 'l_margin_ldist_city' ...
% 'lcasillas_school_ic' 'lcasillas_l_diff_PRI_PAN' 'lcasillas_lpop' 'lcasillas_l_turnout' 'lcasillas_local' 'lcasillas_ldist_city' ...
% 'school_ic_l_diff_PRI_PAN' 'school_ic_lpop' 'school_ic_l_turnout' 'school_ic_local' 'school_ic_ldist_city' ...
% 'l_diff_PRI_PAN_lpop' 'l_diff_PRI_PAN_l_turnout' 'l_diff_PRI_PAN_local' 'l_diff_PRI_PAN_ldist_city' ...
% 'lpop_l_turnout' 'lpop_local' 'lpop_ldist_city' ...
% 'l_turnout_local' 'l_turnout_ldist_city' ...
% 'local_ldist_city' 'ldist_pri' 'gov_PRI' 'ldist_pan' 'gov_PAN'};



if nargin<4
    p_PRI=phats{1,1}(:,1:2); %remember prob H in first, M in second column
    p_PAN=phats{1,2}(:,1:2);

    %Expanded specification
    Z_PAN=X(:,end-1:end);
    Z_PRI=X(:,end-3:end-2);
    X=X(:,1:9);

    
    Y_PAN=Y(:,2);
    Y_PRI=Y(:,1);

    y_PAN=dummyvar(Y_PAN+1);
    y_PRI=dummyvar(Y_PRI+1);


     X_PRI=[X Z_PRI p_PAN ones(size(X,1),1)]; 
     X_PAN=[X Z_PAN p_PRI ones(size(X,1),1)];
    
    beta_p_PAN=(X_PAN'*X_PAN)\(X_PAN'*y_PAN(:,2:3));
    beta_p_PRI=(X_PRI'*X_PRI)\(X_PRI'*y_PRI(:,2:3));

    beta_p=[beta_p_PRI beta_p_PAN];
end   

options = optimoptions('lsqnonlin','Display','iter','Jacobian','on','DerivativeCheck','off','TolX',1e-08,'TolFun',1e-9);
  tic;  
    beta = lsqnonlin(@(b)least_sq(b,X,phats),beta_p(:),[],[],options);
  toc;  
end

